A mathematical method of combining several elements has emerged in recent times, providing a more comprehensive approach. Adhering to the foregoing mathematical methodology, we fuse two extremely potent methods, namely graph theory and neutrosophic sets, and present the concept of neutrosophic graphs ($\aleph G$). Next, we outline many ideas, such as union, join, and composition of $\aleph G$s, which facilitate the straightforward manipulation of $\aleph Gs$ in decision-making scenarios. We provide a few scenarios to clarify these activities. The homomorphisms of $\aleph Gs$ are also described. Lastly, understanding neutrosophic graphs and how Japan responds to earthquakes can help develop more resilient and adaptable disaster management plans, which can eventually save lives and lessen the effects of seismic disasters. With the support of using an absolute score function value, Hokkaido (H) and Saitama (SA) were the optimized locations. Because of its location in the Pacific Ring of Fire, Japan is vulnerable to regular earthquakes. As such, it is critical to customize reaction plans to the unique difficulties and features of Japan’s seismic activity. Examining neutrosophic graphs within the framework of earthquake response centers might offer valuable perspectives on tailoring and enhancing response tactics, particularly for Japan’s requirements.

American scientific publishing group

In this manuscript, we obtain common fixed point theorems in the neutrosophic cone metric space. Also, notion of Φ,Ψ-weak contraction is defined in the neutrosophic cone metric space by using the idea of altering distance function. Finally, we review many examples of cone metric spaces to verify some properties.

In this paper, we apply the notion of $e$-$\I$-open sets \cite{Wadei6} in ideal topological spaces to present and study new classes of functions called contra $e$-$\I$-continuous functions, almost-$e$-$\I$-continuous, almost contra-$e$-$\I$-continuous, and almost weakly-$e$-$\I$-continuous along with their several properties, characterizations and mutual relationships. Relationships between their new classes and other classes of functions are established and some characterizations of their new classes of functions are studied. Further, we introduce new types of graphs, called $e$-$\I$-closed, contra-$e$-$\I$-closed, and strongly contra-$e$-$\I$-closed graphs via $e$-$\I$-open sets. Several characterizations and properties of such notions are investigated.

Wadei Faris Al-Omeri. IJFIS 2020;20:242-6. https://doi.org/10.5391/IJFIS.2020.20.3.242